The definition of DNI is the irradiance on a surface perpendicular to the vector from the observer to the center of the sun caused by radiation that did not interact with the atmosphere (WMO 2008). This strict definition is useful for atmospheric physics and radiative transfer models, but it results in a complication for ground observations: It is not possible to measure whether or not a photon was scattered if it reaches the observer from the direction in which the solar disk is seen. Therefore, DNI is interpreted differently in the world of solar energy. Direct solar radiation is understood as the “radiation received from a small solid angle centered on the sun’s disk” (ISO 1990). The size of this “small solid angle” for DNI measurements is recommended to be 5 ∙ 10-³ sr (corresponding to and approximate 2.5-degree half angle) (WMO 2008). This
recommendation is approximately 10 times larger than the radius of the solar disk itself (yearly average 0.266 degree). This is because instruments for DNI measurements (pyrheliometers) have to track or follow the sun throughout its path of motion in the sky, and small tracking errors have to be expected. The large field of view (FOV) of pyrheliometers reduces the effect of such tracking errors.
To understand the definition of DNI and how it is measurement by pyrheliometers in more detail, the role of circumsolar radiation has to be discussed. Because of forward scattering of direct sunlight in the atmosphere, the circumsolar region closely surrounding the solar disk (solar aureole) looks very bright. The radiation coming from this region is called circumsolar radiation. For the typical FOV of modern pyrheliometers (2.5 degrees), circumsolar radiation contributes a variable amount, depending on atmospheric conditions, to the DNI measurement. This
contribution can be quantified if the radiance distribution within the solar disk angle and the circumsolar region and the so-called penumbra function of the pyrheliometer is known. Both of these bits of information will be explained in the following. Such an explanation is of particular interest for concentrating solar technologies (CSP or CPV), because the contribution of
circumsolar radiation to the yield of most concentrating power plants is less than the contribution from the DNI measurement. This effect has to be considered in the performance analysis of concentrating collectors to avoid overestimating the intercepted irradiance.
The first bit of information that is required to determine the effect of circumsolar radiation on the pyrheliometer is the solar and circumsolar radiance distribution. This distribution usually shows good radial symmetry around the center of the sun. Thus, it can be accurately described as a function of the angular distance from the center of the sun. This solar radiance profile, normalized to unity in the center of the sun, is called sunshape. The sunshape not varies with time and sky conditions, and the average sunshape determined for a specific site can also be very different from that of another location.
The solar radiance profile has been of interest for scientists of various specializations already for some centuries. In the middle of the 18th century, Bouguer carried out measurements of the disk radiance profile and found that the radiance decreases with increasing angular distance from the center of the sun (Mueller 1897). Between 1920 and 1955, the Smithsonian Institution measured the circumsolar irradiance coming from an annular region concentrically positioned around the sun under the lead of Dr. C.G. Abbot (Watt 1980).
Measurements of the solar radiance profile including the solar disk and the circumsolar region have been carried out by Lawrence Berkeley National Laboratory (LBNL) (Grether, Nelson, and
Wahlig 1975). The measurements from LBNL are of special importance for solar energy,
because nearly 180,000 measurements were collected from 11 different sites in the United States between 1976 and 1981 and were later digitally published in the LBNL reduced data base
(Noring, Grether, and Hunt 1991). The instrument had a small circular aperture and measured the radiance coming from nearly point-like regions around and inside the solar disk. Other groups used analog photographic techniques to determine the solar radiance profile (for example, Deepak and Adams [1983] and Sandia National Laboratories [see Watt {1980}]). In the 1990s, charge-coupled device cameras were used by the Paul Scherrer Institute and the German Aerospace Center (DLR) (Schubnell 1992), an approach that was followed later by DLR until the end of the last century (Neumann et al. 1998). Recently, a method based on two commercial instruments (Visidyne’s sun and aureole measurement system, Sytem Advisor Model (SAM), and a CIMEL sun photometer) was presented (Wilbert, Pitz-Paal, and Jaus 2013). Other instruments that measure the circumsolar irradiance are documented in Wilbert, Pitz-Paal, and Jaus (2012); Wilbert, Pitz-Paal, and Jaus (2013); Kalapatapu et al. (2012); and Wilbert (2014). Figure 2-7 shows sunshapes derived from LBNL and the first DLR sunshape measurement system. Averages throughout several measurements are shown. A proposed “standard solar scan” was determined by Rabl and Bendt (1982) as an average from LBNL measurements. The term “standard” should not be misunderstood. Here it refers to an average of many sunshapes that deviate strongly from the so-called “standard solar scan.” “DLR mean” shows an average sunshape derived from DLR’s measurements as presented under this name in (Neumann et al. 2002). The other sunshapes are averages of sunshapes within different intervals of CSRs (circumsolar ratio) from (Neumann et al. 2002). They are named corresponding to the CSR interval that was used for the averaging. The CSR can be used to characterize the sunshape to some extent (Buie and Monger 2001). It is defined as
CSR(adisk, alim) = CSNI(adisk, alim) / (CSNI(adisk, alim) + DNI(adisk)) (2-2) Here, CSNI(adisk, alim) is the circumsolar normal irradiance observed in the circumsolar region between the angular distances adisk and alim from the center of the sun. adisk is the solar disk angle (half angle), and DNI(adisk) is the disk irradiance (the normal irradiance caused by the radiation observed within the angular distance adisk around the sun’s center, independent of
whether or not the photons were scattered).
The extent of the circumsolar region cannot be defined in a universally valid way. This is because different pyrheliometers and different concentrating collectors use radiation up to individual angular distances alim from the center of the sun. Hence, alim has to be selected depending on the investigated technology. For example, alim = 3.2° is used for the CSR in the LBNL reduced database (Noring et al. 1991), and ≥ 4° would be necessary to allow the complete description of a pyrheliometer measurement following World Meteorological Organization (WMO) recommendations (see next paragraph on penumbra functions).
For the physically exact interpretation of the CSR, adisk is calculated as a function of time using the visible disk radius and the time dependent distance between the sun and the Earth (Wilbert,
path around the sun. For the LBNL data, a slightly higher angle than the average solar disk angle is used for all measurements (Watt 1980) to avoid instrumental errors that caused an
overestimation of the radiance close to the solar disk angle.
For CPV applications also, the spectral variation of the CSR has to be considered. Spectral CSR values for different wavelengths deviate strongly from each other and also from the
corresponding broadband CSRs (Evans et al. 1980). Average ratios of broadband CSR to spectral CSR between 0.7 and 1.4 have been found for the visible and near-infrared spectrum with the LBNL instrument (for measurements around noon). The spectral dependence of these average ratios found for low CSR levels is opposite to that for high CSRs. Also, the scatter of these ratios for each of the wavelengths investigated by LBNL was quite high (Evans et al. 1980). Similar ratios were found in an analysis based on sunshapes predicted by the three-dimensional Monte Carlo radiative transfer model MYSTIC (Mayer 2009) that is part of the libRadtran package (Mayer and Kylling 2005) and SMARTS2 (Gueymard 2001) in Wilbert, Pitz-Paal, and Jaus (2013). Further, the broadband CSR and especially the spectral CSR depend on the AM.
Figure 2-7. Different sunshapes from Rabl and Bendt (1982) and Neumann et al. (2002). The average solar disk angle and the recommended FOV of a pyrheliometer (WMO 2008) are shown as
vertical lines. Image from Stefan Wilbert, DLR
The other bit of information to determine the effect of the circumsolar radiation on the DNI measurement is the penumbra function of the pyrheliometer. For pyrheliometers, the geometrical penumbra function evaluated at an angular distance a a from the center of the sun Ppyr(a) is
defined as the fraction of parallel rays incident on the pyrheliometers aperture at a that reaches the sensor element. It can be calculated using the distance between the aperture window and the sensor element and their respective sizes (Pastiels 1959). Penumbra functions are defined equivalently to angular acceptance functions for CSP or CPV plants, for example, as used in Rabl and Bendt (1982).
All radiation is detected for angular distances between 0 degrees and the slope angle aslope. For
angular distances greater than the limit angle alim, no radiation is detected by the instrument. The
opening half angle (also FOV) is defined as the angle between the optical axis of the instrument and the vector from the center of the sensor element to the border of the instrument’s entrance aperture. The opening angle is the average of the slope and the limit angle. WMO recommends that pyrheliometers should have an FOV of 2.5 degrees, a slope angle of 1 degree (WMO 2008), and it follows that the limit angle should be 4 degrees (all angles given as half angles).
Taking into account effects such as the spatial inhomogeneity of the sensor in addition to the geometry, the effective angular acceptance function is obtained (Major 1994).
The radiation accepted by a pyrheliometer DNIexp for a known radially symmetric solar radiance profile Lsolar can be calculated as:
∫
⋅ = limLsolar Ppyr d a a a a a a p 0exp 2 ( ) ( )sin( )cos( )
DNI (2-3)
In this handbook, we understand DNI as DNIexp following the typical usage in solar energy. Circumsolar radiation data are available from the LBNL Reduced Data Base.4 A detailed discussion of circumsolar radiation can be found in Blanc et al. 2014).
With the resurgence of interest in concentrating solar technology, there is a renewed interest and research in the amount of circumsolar radiation, or sunshapes, as affected by the variable
properties of the atmosphere. This is especially relevant for power plant projects in regions in which no sunshape measurements have been performed so far.